The crime novel "Dark of the Moon" by John Dickson Carr has as one of its characters a female "mathematician", Camilla Bruce. (She is called a mathematician and is enthusiastic about the subject but she seems to be some sort of student, if I remember correctly. She is definitely not a professional mathematician.)

She functions as the love interest in the story for the male POV character, who it so happens hate mathematics. Thus we are treated to a few debates on the value of mathematics. Unfortunately the author is rather on the anti-mathematical side and Camilla does not get any very good arguments. On the other hand, a rather typical negative view of mathematics based on school experiences is nicely presented in all its wrongness. Permit me a quote from the POV character (which I must credit Jason Rosenhouse with putting on the net):

(quoted from Dark of the Moon)

"To me mathematics means the activities of those mischievous lunatics A, B, and C. In my time they were always starting two trains at high speed from distant points to see where the trains would collide somewhere between. . . . And when the silly dopes weren’t wrecking trains or computing the ages of their children without seeming to know how old the brats were, two of ‘em had a passion for pumping water out of a tank while the third mug pumped water into it."

The book thus may interest people who are interested in cultural depictions of mathematics, even somewhat negative ones. It is not a very good book however, and I say that as someone who loves much of Carr's work.

Mathematics is a pet hate of Carr by the way, along with socialism and modernist literature, and a number of other of his books have minor characters who are mathematicians. There are even more books of his where people who are not professional mathematicians are called mathematicians anyway, which seems to denote a way of thinking more than a profession to Carr.